Express a 100 kg mass in units of slugs, blobs, and lbm

Express a 100 kg mass in units of slugs, blobs, and lbm. How much does this mass weigh in lbf and in N?

The Correct Answer and Explanation is :

To express a mass of 100 kg in units of slugs, blobs, and lbm, as well as to determine the weight in lbf and N, we will follow these steps:

Step 1: Conversion of mass (100 kg) to slugs, blobs, and lbm

1. Slugs: The slug is the unit of mass in the Imperial system. The conversion factor from kilograms to slugs is:
   [
   1 \text{ kg} = 0.0685218 \text{ slugs}
   ]
   Therefore, to convert 100 kg to slugs:
   [
   100 \text{ kg} \times 0.0685218 \text{ slugs/kg} = 6.85218 \text{ slugs}
   ]
2. Blobs: The blob is a less commonly used unit, mainly in certain physics contexts, defined as:
   [
   1 \text{ blob} = 1 \text{ kg}
   ]
   So, 100 kg is equivalent to 100 blobs.
3. Lbm (Pound Mass): The pound mass (lbm) is a unit of mass in the Imperial system, where:
   [
   1 \text{ kg} = 2.20462 \text{ lbm}
   ]
   Therefore, to convert 100 kg to lbm:
   [
   100 \text{ kg} \times 2.20462 \text{ lbm/kg} = 220.462 \text{ lbm}
   ]

Step 2: Determining weight in lbf and N

Weight is the force exerted by gravity on an object, and is given by the formula:
[
W = m \times g
]
Where:

• ( m ) is mass
• ( g ) is the acceleration due to gravity.

In the Imperial system:

1. To convert from lbm to lbf (pound-force), the standard acceleration due to gravity is approximately 32.174 ft/s²:
   [
   W_{\text{lbf}} = 100 \text{ lbm} \times \frac{32.174 \text{ ft/s}^2}{32.174 \text{ ft/s}^2} = 100 \text{ lbf}
   ]
   So the weight in lbf is 100 lbf.

In the SI system:

1. To convert mass to weight in newtons (N), we use:
   [
   W_{\text{N}} = 100 \text{ kg} \times 9.81 \text{ m/s}^2 = 981 \text{ N}
   ]
   So the weight in N is 981 N.

Summary:

• 100 kg = 6.85218 slugs
• 100 kg = 100 blobs
• 100 kg = 220.462 lbm
• Weight = 100 lbf (in the Imperial system)
• Weight = 981 N (in the SI system)